Transistor Temperature Stability

As the temperature of a transistor increases, the collector current will increase because

Intrinsic semiconductor current between the collector and base increases with temperature. Its flow through the biasing resistors drives the base more positive, increasing forward bias on the base-emitter diode. For a silicon diode Simpson quotes an increase of 2 nA for a 10°C temperature rise.

The base-emitter voltage required for a given collector current will decrease. This decrease is about -2.5 mV/°C.

An approximate relationship for the collector current change is:

An increase in temperature produces an increase in the minority carrier current, but a negative change in VBE, so both effects lead to an increase in collector current with temperature. Since the emitter resistance shows up in the denominator of both terms, this shows that a large value of RE is desirable for
temperature stability.

The presence of RE provides negative feedback which stabilizes the circuit against changes in temperature, supply voltage, etc., but it also decreases the voltage gain.